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Relative left properness of colored operads

Philip Hackney, Marcy Robertson and Donald Yau

Algebraic & Geometric Topology 16 (2016) 2691–2714
Abstract

The category of –colored symmetric operads admits a cofibrantly generated model category structure. In this paper, we show that this model structure satisfies a relative left properness condition, ie that the class of weak equivalences between Σ–cofibrant operads is closed under cobase change along cofibrations. We also provide an example of Dwyer which shows that the model structure on –colored symmetric operads is not left proper.

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Keywords
operads, model categories, left proper
Mathematical Subject Classification 2010
Primary: 18D50, 55U35
Secondary: 18G55, 55P48, 18D20
References
Publication
Received: 1 December 2014
Revised: 9 December 2015
Accepted: 1 February 2016
Published: 7 November 2016
Authors
Philip Hackney
Department of Mathematics
Stockholm University
SE-106 91 Stockholm
Sweden
Marcy Robertson
School of Mathematics and Statistics
University of Melbourne
Melbourne ACT 3010
Australia
Donald Yau
Department of Mathematics
The Ohio State University at Newark
Newark, OH 43055
United States